# LINR 1 | Lesson 1 | Practice (Solutions)

## Practice (Solutions)

### Tables

Complete each section to show your understanding for linear patterns.

The following tables represent linear patterns. The tables are created using Desmos.com.

1. Find the missing values in each table.
• Table 1: (3, 7) and (12,15)
• Table 2: (4, 9) and (21, -42)
• Table 3: (-2, 4) and (8, 24)
2. Graph each table on a coordinate plane.
3. Calculate the slope using the table.
• Table 1: change in $$y$$ is 4 and change in $$x$$ is 1, i.e. slope is 4
• Table 2: change in $$y$$ is -3 and change in $$x$$ is 1, i.e. slope is -3
• Table 3: change in $$y$$ is 2 and change in $$x$$ is 1, i.e. slope is 2
4. Calculate the slope using the graph.
5. Determine the point of the $$y$$ intercept.
• Table 1: (0,-5)
• Table 2: (0,18)
• Table 3: (0,8)
6. Write an equation to determine the $$y$$value given any $$x$$-value.
• Table 1 equation: $$y = 4x -5$$
• Table 2 equation: $$y=21 – 3x$$
• Table 3 equation: $$y= 2x + 8$$

### Patterns

Given the growth pattern shown in Figure 2 and Figure 4.

1. Draw Figure 3.
• Figure 3 has 3 rows of 6, so a row of 6 is added to Figure 2.
2. Explain the growth pattern.
• 6 is added each time.
3. Determine the number of squares in Figure 0.
• Figure 0 has 1 square.
4. Write the equation to represent the number of squares for any figure.
• $$1 + 6n$$, where $$n$$ is the figure number.
5. Using the context of growth patterns, explain why $$m$$ represents the slope and $$b$$ represents the $$y$$-intercept in the slope-intercept formula $$y=mx+b$$.
• The slope is 6 since, 6 squares are added to create the next figure. To find the $$y$$-intercept we need to find the number of squares in Figure 0 which can be found by subtracting 6 squares from Figure 2 to find Figure 1, and another 6 squares from Figure 1 to find Figure 0, or 13-6-6 = 13-12 = 1. Therefore 1 is the $$y$$-intercept.

A given linear pattern has 10 squares in Step 3.  The pattern grows by -4 squares every 2 steps.

1. Create a table for this pattern.
2. Calculate the slope to represent the growth for this pattern.
• Slope is -4
3. Calculate the equation to calculate the number of squares for each step.
• $$y = 22 – 4x$$